Astronomical polarimetry is an area currently undergoing much study and development, at least in part responsive to high-sensitivity searches for “B-modes” of the cosmic microwave background radiation polarization.
The cosmic microwave background is polarized at the level of a few microkelvins. There are two types of polarization, respectively known as E-modes and B-modes. The relationship between these modes may be analogous to electrostatics, in which the electric field (E-field) has a vanishing curl and the magnetic field (B-field) has a vanishing divergence. The E-modes arise naturally from Thomson scattering in inhomogeneous plasma. The B-modes, which are thought to have an amplitude/magnitude of at most a 0.1 μK, are not produced from plasma physics alone.
Detecting the B-modes is extremely difficult, particularly given that the degree of foreground contamination is unknown, and the weak gravitational lensing signal mixes the relatively strong E-mode signal with the B-mode signal.
B-modes are signals resulting from cosmic inflation and are determined by the density of primordial gravitational waves. B-modes thus provide signatures for gravitational waves associated with the inflationary epoch and are expected to provide a direct measurement of the energy scale of inflation. Amplitudes for B-modes are theorized to be on the order of 10−7 to 10−9 of that of the cosmic background radiation, and thus measurement of the B-modes requires a robust modulation strategy and effective control over systematic artifacts.
Emission from magnetically-aligned dust in our Galaxy contributes to interference that will have to be understood in order to clearly distinguish and extract the B-mode from the total signal. However, this polarized emission also provides a tool for analyzing the role of magnetic fields in star formation. The advent of multiple wavelength submillimeter and far-infrared photometers, such as SCUBA2 (a new generation submillimeter imager for the James Clerk Maxwell Telescope) and HAWC (a far-infrared camera for the Stratospheric Observatory For Infrared Astronomy (SOFIA)), provides opportunity to expand such study. Polarization modules have been developed to facilitate leveraging of these new photometric tools for such applications by allowing them to function as polarimeters.
Partial polarization results from statistical correlation between the electric field components in the plane perpendicular to the propagation direction. Such correlation is represented via complex quantities, and, as a result, in measurements of polarized light, it is convenient to employ linear combinations of these correlations, such as Stokes parameters, e.g., I, Q, U and V.
The polarization state of radiation through an optical system may be modeled by determining the transformations that describe the mapping of the input to the output polarization states. In modeling the types of optical elements associated with the polarization modules described in this disclosure, Stokes I is decoupled from the other Stokes parameters. For this class of elements, the polarization P, as described with reference to Eq. (1) below,P2=Q2+U2+V2,  (1)is constant. Eq. (1) may be interpreted to describe the points on the surface of a sphere in three-dimensional space having Q, U and V as coordinate axes. This sphere is known as the Poincaré sphere, and the action of any given ideal polarization modulator may be described by a rotation and/or an inversion in this space. Such operations correspond to introduction of a phase delay between orthogonal polarizations, and that is the physical mechanism operative in a polarization modulator. The two degrees of freedom of any given transformation are the magnitude of the introduced phase delay and a parameter describing the basis used to define the phase delay. These two parameters directly define the orientation and the magnitude of the rotation on the Poincaré sphere: the rotation axis is defined by the sphere diameter connecting the two polarization states between which the phase is introduced, and the magnitude of the rotation is equal to that of the introduced phase.
In order to measure the polarized part of a partially-polarized signal, it is useful to separate the polarized portion of the signal from the unpolarized portion. This is especially useful when the fractional polarization is small. One way to do this is to methodically change, or modulate, the polarized portion of the signal (by changing one of the parameters of the polarization modulator) while leaving the unpolarized portion unaffected. Periodic transformations in Poincaré space can accomplish this encoding of the polarized portion of the signal for subsequent demodulation and detection. A convenient way of formulating the problem is to envision a detector that is sensitive to Stokes Q when projected onto the sky in the absence of modulation. The polarization modulator is then systematically changing the polarization state to which the detector is sensitive. By measuring the output signal, the polarization state of the signal or light may be completely characterized.
One conventional way to implement such a polarization modulator is by use of a dielectric birefringent plate. A birefringent plate comprises a piece of birefringent material cut so as to delay one linear polarization component relative to the other by the desired amount (generally either one-half or on quarter of the wavelength of interest). In this case, the phase difference is fixed, and the modulation is accomplished by physically rotating the birefringent plate (and hence the basis of the introduced phase).
However, a birefringent plate may be built to measure either circular or linear polarization, but cannot measure both. Additionally, polarization modulators built using this approach are not readily retuned for use at multiple wavelengths. Further, the requirement to be able to rotate the birefringent plate engenders need for a complex ensemble of shafts, bearings and gears.
For the reasons stated above, and for other reasons discussed below, which will become apparent to those skilled in the art upon reading and understanding the present disclosure, there are needs in the art to provide improved phase modulators in support of increasingly stringent and exacting performance and measurement standards in settings such as astronomical observation.